Hardness of deriving invertible sequences from finite state machines

• Many test generation algorithms use unique input/output sequences (UIOs) that identify states of the finite state machine specification M. However, it is known that UIO checking the existence of UIO sequences is PSPACE-complete. As a result, some UIO generation algorithms utilise what are called invertible sequences; these allow one to construct additional UIOs once a UIO has been found. We consider three optimisation problems associated with invertible sequences: deciding whether there is a (proper) invertible sequence of length at least K; deciding whether there is a set of invertible sequences for state set S′ that contains at most K input sequences; and deciding whether there is a single input sequence that defines invertible sequences that take state set S″ to state set S′. We prove that the first two problems are NP-complete and the third is PSPACE-complete. These results imply that we should investigate heuristics for these problems. © Springer International Publishing AG 2017.

Subject headings

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

Keyword

Software testing

Generation algorithm

Input sequence

NP Complete

Optimisation problems

PSPACE-complete

Single input

Test generation algorithm

Unique input/output sequences

Optimization

Publication and Content Type

ref (subject category)

kon (subject category)